×
Log in to StudySoup
Get Full Access to Math - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Math - Textbook Survival Guide

Prove that for the system dx dt = F( x, y), dy dt = G( x, y) there is at most one

Elementary Differential Equations and Boundary Value Problems | 11th Edition | ISBN: 9781119256007 | Authors: Boyce, Diprima, Meade ISBN: 9781119256007 392

Solution for problem 22 Chapter 9.2

Elementary Differential Equations and Boundary Value Problems | 11th Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Elementary Differential Equations and Boundary Value Problems | 11th Edition | ISBN: 9781119256007 | Authors: Boyce, Diprima, Meade

Elementary Differential Equations and Boundary Value Problems | 11th Edition

4 5 1 370 Reviews
23
5
Problem 22

Prove that for the system dx dt = F( x, y), dy dt = G( x, y) there is at most one trajectory passing through a given point ( x0, y0). Hint: Let C0 be the trajectory generated by the solution x = 0(t), y = 0(t), with 0(t0) = x0, 0(t0) = y0, and let C1 be the trajectory generated by the solution x = 1(t), y = 1(t), with 1(t1) = x0, 1(t1) = y0. Use the fact that the system is autonomous, and also the existence and uniqueness theorem, to show that C0 and C1 are the same. 2

Step-by-Step Solution:
Step 1 of 3

F L.*..i,,,r^:f'L 5 i,,...t'lC; { I i rt,(.!/, r',rl-s '1., # ipt,,,,loptr)t/Lr. 11, 5r-i;,,,- a e" lrJ Vr'^4,...

Step 2 of 3

Chapter 9.2, Problem 22 is Solved
Step 3 of 3

Textbook: Elementary Differential Equations and Boundary Value Problems
Edition: 11
Author: Boyce, Diprima, Meade
ISBN: 9781119256007

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Prove that for the system dx dt = F( x, y), dy dt = G( x, y) there is at most one

×
Log in to StudySoup
Get Full Access to Math - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Math - Textbook Survival Guide
×
Reset your password